A New Synchronous Lower Bound for Set Agreement

Abstract. We have a new proof of the lower bound that k-set agreement requires f/k + 1 rounds in a synchronous, message-passing model with f crash failures. The proof involves constructing the set of reachable states, proving that these states are highly connected, and then appealing to a well-known topological result that high connectivity implies that set agreement is impossible. We construct the set of reachable states in an iterative fashion using a round operator that we define, and our proof of connectivity is an inductive proof based on this iterative construction and using simple properties of the round operator. This is the shortest and simplest proof of this lower bound we have seen.

• Type: Conference
• Year: 2001
• Where: WDAG
• Authors: Maurice Herlihy, Sergio Rajsbaum, Mark R. Tuttle
• Keywords: Agreement Requires F/k, Algorithms, Lower Bound, Reachable States, WDAG 2001